CRACK DEPTH MEASUREMENT IN CONCRETE USING SURFACEWAVE TRANSMISSION

J.S. Popovics and J. Zhu

Civil & Environmental Engineering DepartmentThe University of Illinois205 N. Mathews Ave., MC-250Urbana, IL 61801

ABSTRACT. A technique to estimate the depth of surface-breaking cracks in concrete is presented.The surface wave transmission coefficient across the crack plane is determined and used to estimatethe depth. A self-compensating testing scheme is applied to eliminate experimental difficulties. Herethe self-compensating testing scheme is introduced, and the approach used to estimate crack depthfrom the measured surface wave transmission coefficient is described. Experimental resultsobtained from concrete specimens with pre-placed surface-breaking notches are then presented.

BACKGROUNDTechniques that non-destructively detect defects, measure the mechanical properties, or

monitor the state of deterioration in concrete structures are of considerable interest to civilengineers [1,2]. A distinct single surface-breaking crack is a common and significantdefect that can eventually lead to failure of a concrete structure. Thus it is important tomonitor in a non-destructive fashion the distance that the crack extends into the concrete.Several studies on the time-of-flight technique to predict surface-breaking crack depth inconcrete have been reported. The time-of-flight method however is not effective whenrealistic concrete cracks are tested, that is when the crack tip is ill defined and the crack istightly closed [3].

Wave transmission or attenuation measurements do show high sensitivity to realisticcracking in concrete under laboratory conditions [4]. Practical one-sided surface wavetransmission coefficient measurements in relatively homogeneous materials such as metalshave been achieved through the use of a self-compensating testing scheme. In this paper,the surface wave transmission coefficient obtained using a self-compensating scheme isused to predict the depth of surface-breaking notches in concrete.

SELF-COMPENSATING THEORYIn the frequency domain, we can represent the surface wave signal sent at point i and

received at point j (Vy) as a simple product of terms

CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00

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y = A1dSSj (1)where AI describes the source, Sj the receiver and dy the general signal transmissionbetween points i and j. Consider a surface wave traveling from point 1 to 3, as illustratedschematically in Figure 1. The wave travels from point 1, where it is generated asdescribed by the AI term. The wave propagates past point 2 to point 3, where it is receivedas described by the 83 term. The general signal transmission between the points isdescribed by the product di2 d23. If a surface-breaking crack is located immediatelybetween points 2 and 3, it also will affect the signal received at point 3. The effect of thecrack is contained in the surface wave transmission coefficient T, which represents theratio of transmitted wave amplitude to incident surface wave amplitude as a result of waveinteraction with that particular crack. Thus

Vi3 = T d23 S3. (2)

Similar expressions are derived for Vi2, V43 and V42. By obtaining four signals, we mayeliminate the extraneous source and receiver terms and outlying material signaltransmission terms that are normally coupled in the signal with the simple manipulation

= (V42Vi3/V43V12)'0.5 (3)

A complementary measurement over a crack-free region of the same material gives anexpression for d23. Thus T may be determined by the quotient of the crack and crack-freetransmission data sets by eliminating d23. This final expression gives the transmissioncoefficient of the crack as a function of frequency. Further detail on the approach,including required signal processing, is given by Popovics et al. [5].

Because the manipulations are carried out in the frequency domain, one can useindividual wave pulses that contain a broad range of frequencies, thereby providing moredata to use in the computations. When using broad-band signals in concrete, it is importantto define the region of acceptably high signal to noise ratio within a given function is ameasure of the variability of repeated and nominally identical transmission data, from the

FIGURE 1. Plan view of self-compensating testing configuration showing source (circle) and receiver(squares) point locations with respect to the crack.

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same testing location, computed at each frequency. High variability at a given frequencyindicates poor (low) signal to noise ratio and therefore unreliable data. Conversely, lowvariability indicates reliable data. The signal consistency function is the quotient of thegeometric and arithmetic averages of the repeated data in the frequency domain. Previouswork indicates that acceptable signals are provided when signal consistency greater than0.99 at a given frequency is achieved [5]. An example signal consistency plot from anotched concrete slab is shown in Figure 2; the acceptable frequency region (5 kHz to 48kHz) is indicated.

MODEL AND VERIFICATIONPrevious work suggests that signal wave transmission is a sensitive indicator of surface-

breaking crack depth: signal transmission decreases at all frequencies as crack depthincreases. A unique relation between surface wave transmission coefficient and surface-breaking crack depth normalized by the surface wave wavelength at a given frequency (a*)has been observed in previous work on cracked concrete slabs (crosses in Figure 3) andverified by boundary element (BEM) computations for a crack (solid line in Figure 3) [6].These experimental results were obtained using the self-compensating scheme describedabove, where the tests were performed on actual cracks in concrete slabs. The work showsthat T drops rapidly as a* increases from 0 to approximately 0.4. As a* increases beyond0.4, T declines at a much slower rate, and also fluctuates, until it reaches a relativelyconstant value for a* > 1.3. Note that the data indicate that T > 0.22 for a* < 0.4. Also itwas found that the notch and cracked cases give similar response for T > 0.4.

0.950 10000 20000 30000 40000 50000 60000

Frequency, hk

FIGURE 2. Signal consistency function obtained from concrete slab with 49 mm notch.

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X Experiment

——BEM

0 0.5 1 1.5 2

Normalized crack depth aAR

FIGURE 3. Experimental data (points) using self-compensating scheme and numerical prediction (line) ofrelation between T and a* in concrete slabs containing surface breaking cracks.

INVERSION APPROACHThe observed relation between T and normalized crack depth suggests a possible

approach for the measurement of in situ crack depth (a). Self-compensating measurementscan be used to determine T. But then we need to develop an approach for inversion of thedata to solve for a from T. Here we use the relation between T and normalized crack deptha* as determined by the BEM analysis. A unique and sensitive region of the observedrelation for this purpose is provided when a* < 0.35. A least-squares best-fit second-ordercurve to the data in this region is given by

T = -2.2 a*2 -1.8 a* + 1.0. (4)

Inverse expressions for a* are easily obtained from Eqn. 3 using the quadratic equation.Based on these observations, the following approach is used to determine a fromexperimentally-obtained values of T:

(1) Record T at each frequency datum that admits acceptable signal consistency and forall values of T> 0.4

(2) Compute a* for each accepted value of T using the inverse expressions of Eqn.3.(3) Compute a from a* using an appropriate value of wavelength at each frequency

datum. (Wavelength computed from quotient of surface wave velocity (constant)and frequency).

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The described approach provides multiple redundant estimates of a from admissible data ateach frequency. The redundant values are averaged to provide a single estimate of a.

EXPERIMENTSExperiments were carried out in order to verify the proposed inversion approach to

determine a from T obtained with the self-compensating approach.

Testing Setup and SpecimensTests were carried out on concrete slabs that are 150cm x 150cm x 22cm in dimension.

The slabs are comprised of normal Portland cement concrete having a maximum aggregatesize of 25mm. 5mm wide notches of varying depth were cut into the top surface at thecenter of each slab. Test results from slabs with three notch depths are reported here:20mm, 49mm and 99mm. The notch depths were verified by direct examination. Thesurface wave velocities of each concrete slab were measured [7] and found to beapproximately 2250 m/s in all cases. This constant value was used in the computations.

The surface waves were generated by the impact of small steel spheres on the surface ofthe concrete. The tests were repeated for a 5mm sphere source and a 12mm sphere source.The impact events were applied to locations 1 and 4 (see Fig. 1). The surface waves weredetected by miniature accelerometers mounted directly on the concrete surface at locations2 and 3 (see Fig. 1). The accelerometers have nominal sensitivity of 1.02 mV/(m/s2) andnominal ±10% flat frequency response over 1 to 25 kHz. The spacings between adjacentpoints are 30mm, and the notch was centrally located between points 2 and 3. The transientsignals were captured by a digital oscilloscope (signal duration of 100 (isec, digitized withsampling frequency of 5.12 MHz) and transferred to a computer via the GPIB connection.Further data processing was carried out with a Lab Windows program on the computer.

Results From Concrete SpecimensExperimental data obtained across the 20mm notch (a = 20mm) are shown in Fig. 4. In

the plot, T values obtained using the self-compensating method are plotted in terms of a*;a* is derived from known values of a and frequency. The data for the repeated cases of the5mm and 12mm diameter spheres are shown as points and the predicted BEM response(Eqn. 3) is shown as a line. The limit of acceptable signal consistency for this test isdenoted by the dashed line; the usable region for the inversion approach is that above andto the right of the dotted lines. The data from the two impactors are in good agreementwithin the usable region; this illustrates the effectiveness of the self-compensatingapproach in eliminating the effects of varying source characteristics. The agreementbetween the experimental data and BEM prediction is reasonable within that same region.Each experimental datum within the usable region provides a prediction of a, and theseredundant predictions are averaged to provide a single prediction. The average predicteddepths are shown in Table 1; for the case of a=20mm, an error of 5mm is obtained. Theerror for a = 49 is only 1mm. This level of error is acceptable for crack depth estimation inconcrete.

The data for a=99mm is shown in Fig. 5. In this case we see that no data fall within theacceptable region, and therefore no depth prediction can be made with the describedapproach. The reason for this shortcoming is the difficulty we encountered in obtainingconsistent and usable data, as defined by the signal consistency function, at lowfrequencies. With the described approach, low frequency data are needed in order to size

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Small impactor (5mm OD)

arge impactor (12mm OfD)

0.05 0.1 0.15 0.2 0.25Normalized notch depth, a*

0.35

FIGURE 4. Experimental data (points) using self-compensating scheme and numerical prediction (line) (ofrelation between T and a* in concrete slabs containing 49mm surface breaking notch. Usable region isdefined above and to the right of the dotted lines.

deep notches. For example, our minimum consistent frequency data obtained by anexperiment was 5 kHz. At this frequency, the largest crack depth that can be sized with thedescribed approach is 115mm. In the case of a=99, the minimum usable frequency washigher, so it could not be sized. In order to size deeper cracks, consistent data at lowerfrequencies must be obtained. We are currently investigating alternative wave sources inorder to obtain the needed consistency at low frequencies.

CONCLUSIONSThe following conclusions are drawn based on the results presented in this paper:(1) The self-compensating testing scheme allows reliable measurement of wave

transmission (T) for surface waves interacting with surface-breaking cracks andnotches in concrete slabs.

(2) T can be related to notch depth in concrete assuming appropriate frequency rangesof data with acceptable signal consistency can be obtained.

TABLE 1. Comparison of predicted and actual notch depths for the 5mm sphere impactor.

Actual notch depth(mm)

204999

Predicted depth(mm)

1548

****

Error(mm)

51

****

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Large impactpr (12 mm OD)

0.2 0.4 0.6Normalized notch depth, a*

0.8

FIGURE 5. Experimental data (points) using self-compensating scheme and numerical prediction (line) (ofrelation between T and a* in concrete slabs containing 99mm surface breaking notch. Usable region isdefined above and to the right of the dotted lines.

(3) The approach provides predictions with acceptable accuracy for small and mediumnotch depths.

(4) The experimental aspects of the approach must be improved in order to measure thedepth of deep cracks and notches since acceptable signal consistency is difficult toobtain at low frequencies.

REFERENCES1.

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CRC Handbook on Nondestructive Testing of Concrete, edited by V.M. Malhotraand N.J. Carino, CRC Press, Boca Raton, 1991.Bungey, J.H. and Millard, S.G., Testing of Concrete in Structures, 3rd edition,Blackie Academic & Professional, London, 1996.Song, W., Popovics, J.S. and Achenbach, J.D., "Crack depth determination inconcrete slabs using wave propagation measurements", in Proceedings of theFederal Aviation Administration Technology Transfer Conference, Atlantic City,NJ, April 1999.Suaris, W. and Fernando, V., "Ultrasonic pulse attenuation as a measure of damagegrowth during cyclic loading concrete", ACIMaterials Journal, 84, 185-193(1987).Popovics, J.S., Song, W., Ghandehari, M, Subramaniam, K.V., Achenbach, J.D.and Shah, S.P., "Application of wave transmission measurements for crack depthdetermination in concrete", ACI Materials Journal, 97, 127-135 (2000).Song, W., Popovics, J.S., Aldrin, J.C., and Shah, S.P., "Measurement of surfacewave transmission coefficient across surface-breaking cracks and notches inconcrete," submitted to Journal of the Acoustical Society of America. In review.Popovics, J.S., Song, W., Achenbach, J.D., Lee, J. and Andre, R.F., "One-sidedstress wave velocity measurement in concrete," ASCE Journal of EngineeringMechanics, 124, 1346-1353 (1998).

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